derivative f(x)= 3/8 x^4-2-(10)/x

Lösung

ableitung von

f (x) = \frac{3}{8} x^{4} - 2 - \frac{10}{x}

\frac{3 x ^{3}}{2} + \frac{10}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{8} x^{4} - 2 - \frac{10}{x})

Vereinfache

\frac{3}{8} x^{4} - 2 - \frac{10}{x} : \frac{3 x ^{4}}{8} - 2 - \frac{10}{x}

= \frac{d}{d x} (\frac{3 x ^{4}}{8} - 2 - \frac{10}{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{3 x ^{4}}{8}) - \frac{d}{d x} (2) - \frac{d}{d x} (\frac{10}{x})

\frac{d}{d x} (\frac{3 x ^{4}}{8}) = \frac{3 x ^{3}}{2}

\frac{d}{d x} (2) = 0

\frac{d}{d x} (\frac{10}{x}) = - \frac{10}{x ^{2}}

= \frac{3 x ^{3}}{2} - 0 - (- \frac{10}{x ^{2}})

Vereinfache

= \frac{3 x ^{3}}{2} + \frac{10}{x ^{2}}

d er i v a t i v e f (x) = (3 x^{2} - 1)^{2}

a re a 2 x, y = \frac{1}{3} x

\frac{d}{d x} (x^{3} + 3 x^{2} - 9 x + 4)

x \to 2 lim (k x)

\int 9 - y^{2} d y